Under normal circumstances, the terminal potential difference (also known as the terminal voltage) of a battery is always less than or equal to its electromotive force (emf). However, there are specific scenarios where the terminal potential difference can exceed the emf of a battery.
### Understanding the Terms
1. **Electromotive Force (emf)**: This is the maximum potential difference provided by a battery when no current is flowing through it. It represents the energy per unit charge that the battery can supply.
2. **Terminal Potential Difference**: This is the voltage measured across the terminals of a battery when it is supplying current to an external circuit. It is the actual voltage available for use in the circuit.
### Conditions Where Terminal Potential Difference Exceeds Emf
1. **Battery Charging Scenario**:
- **Description**: When a battery is being charged, the terminal potential difference can exceed the emf of the battery. This happens because the charging source needs to provide a voltage higher than the battery’s emf to force current into the battery. In this process, the terminal voltage of the battery can rise above its original emf.
- **Explanation**: For instance, if you’re using a charger that applies a voltage greater than the emf of the battery (plus some additional amount to overcome internal resistance), the battery will experience a higher terminal voltage. This is because the external voltage (from the charger) is overcoming not only the battery’s emf but also any internal resistance within the battery.
2. **Measurement Errors or Special Conditions**:
- **Description**: In some specific measurement scenarios or due to particular characteristics of the measuring instruments, you might get a reading where the terminal potential difference seems to exceed the emf. For example, if the internal resistance of the battery is very low and the battery is charging, measuring the potential difference across the terminals while the battery is being charged can give a reading that is higher than the emf.
- **Explanation**: This situation is often related to transient effects or measurement inaccuracies rather than a real physical situation where the terminal voltage exceeds the emf under normal operating conditions.
### Key Points
- **Normal Discharge**: When a battery is discharging, the terminal voltage is always less than the emf due to the internal resistance causing a voltage drop.
- **Charging Effect**: During charging, the battery’s terminal voltage can temporarily exceed the emf, but this is a result of the charging process rather than a change in the battery's inherent emf.
- **Internal Resistance**: The internal resistance of the battery plays a crucial role in determining the terminal voltage. During discharge, this resistance causes a drop in terminal voltage compared to the emf. During charging, the applied voltage must be higher than the emf to overcome this resistance and induce current flow.
In summary, the terminal potential difference of a battery can exceed its emf mainly during the charging process. Under typical conditions of discharge, the terminal voltage will always be less than the emf.